Pigeon beats man....

...in the Monty Hall Problem:

Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma

Walter Herbranson & Julia Schroeder
Journal of Comparative Psychology, February 2010, Pages 1-13

Abstract: The “Monty Hall Dilemma” (MHD) is a well known probability puzzle in which a player tries to guess which of three doors conceals a desirable prize. After an initial choice is made, one of the remaining doors is opened, revealing no prize. The player is then given the option of staying with their initial guess or switching to the other unopened door. Most people opt to stay with their initial guess, despite the fact that switching doubles the probability of winning. A series of experiments investigated whether pigeons (Columba livia), like most humans, would fail to maximize their expected winnings in a version of the MHD. Birds completed multiple trials of a standard MHD, with the three response keys in an operant chamber serving as the three doors and access to mixed grain as the prize. Across experiments, the probability of gaining reinforcement for switching and staying was manipulated, and birds adjusted their probability of switching and staying to approximate the optimal strategy. Replication of the procedure with human participants showed that humans failed to adopt optimal strategies, even with extensive training.

For more see our previous posts on the Monty Hall problem.

What does a Savant do for a living?

Financial Times:

Savant – the surname is real, it was her mother’s maiden name – has had a unique claim to fame since the mid-1980s. It was then, almost 30 years after she took a test as a schoolgirl in downtown St Louis, Missouri, that her IQ came to light. In 1985, Guinness World Records accepted that she had answered every question correctly on an adult Stanford-Binet IQ test at the age of just 10, a result that gave her a corresponding mental age of 22 years and 11 months, and an unearthly IQ of 228.

The resulting publicity changed Savant’s life.
...
When I asked her to describe how her mind approaches a problem, she said: “My first thought, maybe not thought, it’s almost like a feeling, is overview … It’s like, almost, a wartime decision. I keep thinking about all of the fronts, what’s supplying what, where are the most important points … ”

The curious thing, as The Browser observes, is "Why is the cleverest person in the world an agony aunt?" Is this the best use of her talents? Granted she still fields more math questions than Ann Landers, but she's become more of an advice columnist every day.

What really seems to have launched her is her explanation of the solution to the Monty Hall Dilemma. She wasn't the first to solve it, although the Financial Times makes it sound that way. If you're not familiar with the problem, you'll want to take a look.

Cognitive dissonance will have to be reassessed

It ain't necessarily so:

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology.

The economist, M. Keith Chen, has challenged research into cognitive dissonance, including the 1956 experiment that first identified a remarkable ability of people to rationalize their choices.

Read it all here.

Teaching Bayes Rule to MBA students a few years back I did what I thought was a rather good job of explaining to them the Monty Hall Problem. (Given the design of the problem, once you choose any door there is a two thirds chance that Monty is constrained and shows you what is behind one of the other doors because the prize is behind the door he did not reveal; you should switch to the door he did not reveal.) They were convinced I had lost my mind. At least I found out they were alive.